Fret positions on the fingerboard of a stringed instrument such as a guitar are laid out according to a traditional formula known as the Rule of the Eighteenth, according to which vibrating string length, i.e., the distance from the nut to the bridge of the guitar, is divided by 18 to locate the first fret spaced from the nut. The remaining string length, i.e., the distance from the first fret to the bridge, is again divided by 18 to locate the second fret. This formula is repeated until all of the frets are placed on the fingerboard.
Unfortunately, the Rule of the Eighteenth is only an approximately accurate method for determining fret placement and does not result in perfect pitch for the tones produced when a string is engaged with a fret and the remaining string length vibrated.
An alternative method for fret placement has been employed, known as the Whole Tone Scale. In the Whole Tone Scale, the distance from the nut to the bridge is divided by 9 to locate the first whole-tone fret spaced from the nut. The remaining string length is then divided by nine to locate the second whole-tone fret. In similar fashion to the Rule of the Eighteenth, this formula of dividing remaining string length by 9 is repeated until all of the frets for producing whole tones are placed on the fingerboard. The Whole Tone Scale suffers from a similar deficiency in that the fret placement does not result in perfect whole tones when the strings are vibrated.
Accordingly, the need still exists for a fingerboard construction for a fretted and stringed instrument such as a guitar which will achieve perfect pitch for the tones produced when a string is engaged with a given fret and the remaining string length vibrated.